Chem$-$B$4/$May $2018$

$04-$Chem$-$A$3,$ Mass Transfer Operations

December $2014$

PART A: ANSWER ONE OF QUESTIONS $1-2$

Note: Four questions constitute a complete paper $($with one from Part $A,$ one from Part B$,$ and two from Part C$)$

A tank containing water has its top open to air. The tank is cylindrical with a diameter of $2ft.$ The liquid level is maintained at a level of $3ft.$ below the top of the tank as shown in the sketch. The surrounding air is at $310K,\frac{1}{b}ar,$ and $40$ percent relative humidity.

a$)$ What is the molar concentration of water at the top of the tank, i$.$e$.z=0?$

b$)$ What is the molar concentration of water in the vapour phase at the air$-$water interface, i$.$e$.z=L?$

Jote: Molecular weight of air $=28\mathrm{.}9$

Molecular weight of water $=18\mathrm{.}0,$ density of water at $310K=997k\frac{g}{m^3}$

Vapour pressure of water at $310K=\frac{0\mathrm{.}06221}{b}ar,\frac{1}{b}ar={10}^{5}Pa.$

Pulverized coal pellets, which may be approximated as carbon spheres of radius $r_0=1mm,$ burned in air at $1500K$ and $1\mathrm{.}0$atm. Oxygen is transferred to the particle surface by fusion, where it is consumed in the reaction $C+O_{2}C{O}_2.$ The diffusivity $D_{AB}$ for oxygen is $1\mathrm{.}8{10}^{-4}\frac{m^2}{s}.$ Assuming the surface reaction rate to be infinite and neglecting the chan he radius of the pellet, determine the steady$-$state molar consumption rate of oxygen in $o\frac{l}{s}.$